The quantization of this theory has been studied for a long time [1]}, [2]}, [3]}, [4]}, and was De Witt in [4]} the first one who derived the Feynman rules in a Lorentz covariant form.
From dimensional analysis one can notice that \([\kappa ]=-1\) , so this is a non-renormalizable theory.
Hence, if one is interested in studying scattering processes involving gravitons, increasing the number of loops one encounters an increasing number of divergences, which can be removed by adding a set of counter-terms to the action. More precisely, if we decide to work in dimensional regularization, with \(d\)  the continuous dimensions of spacetime, an appropriate suppression of all the divergences at one loop order can be effectively obtained by adding to \(S_{EH}\)  the following counterterm [6]}:
\(\Delta S = \frac{1}{8\pi ^2 \epsilon }\int d^4 x \sqrt{-g}\left(\frac{R^2}{120}+\frac{7}{20}R_{\mu \nu }R^{\mu \nu }\right) \ ,\) 
